Sum of Two Positive Integers

Hard Problem Solving Arithmetic

What is the sum of two positive integers, $a$ and $b$?

1. The product $ab$ is 48.

2. The difference $|a - b|$ is 4.

Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

Both statements (1) and (2) together are sufficient, but neither statement alone is sufficient.

Each statement alone is sufficient.

Statements (1) and (2) together are not sufficient.

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